Your comment makes me wonder why Mexico doesn’t have a launch facility. And if I remember correctly Costa Rica actually builds rocket parts.
Also I believe equatorial orbits are still possible to achieve from USA launch sites, it just means more fuel/ reduced payload.
Interestingly, the James Webb telescope was launched from French Guiana, which is almost right on the equator.
Also Israel is one of the few countries that regularly launches their rockets to the west, as they only have a West Coast.
For example, even though Rocket Lab was founded in New Zealand it is now a US based company. It operates launch facilities both in New Zealand and the US and pretty sure it builds stuff in both countries.
2) In the case of the rocket, it accelerates eastward. Even if parts fall off, and they slow down because of the drag of the atmosphere, and they slow down all the way to the speed of the atmosphere, the atmosphere is more or less moving eastward at the same speed as the earth's rotation, so any part would be unlikely to land any further west than where it detached from the rocket. And if there was no atmosphere on earth any part that fell off a rocket during its ascent to orbit would fall according to a ballistic trajectory and would most certainly land farther east than where it fell.
I assume we don't launch out of Mexico because rocket technology is tightly controlled by ITAR, so there's no way the government would allow any of it to go to another country's sovereign territory.
I assume shipping to the launch pads is a major issue, especially for the Apollo, Space Shuttle and SLS programs which were/are build all over the place in the continental US.